{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hyper-Pyramid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's set up some environmental dependencies. These just make the numerics easier and adjust some of the plotting defaults to make things more legible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python 3 compatability\n",
    "from __future__ import division, print_function\n",
    "from six.moves import range\n",
    "\n",
    "# system functions that are always useful to have\n",
    "import time, sys, os\n",
    "\n",
    "# basic numeric setup\n",
    "import numpy as np\n",
    "\n",
    "# inline plotting\n",
    "%matplotlib inline\n",
    "\n",
    "# plotting\n",
    "import matplotlib\n",
    "from matplotlib import pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# seed the random number generator\n",
    "np.random.seed(121)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# re-defining plotting defaults\n",
    "from matplotlib import rcParams\n",
    "rcParams.update({'xtick.major.pad': '7.0'})\n",
    "rcParams.update({'xtick.major.size': '7.5'})\n",
    "rcParams.update({'xtick.major.width': '1.5'})\n",
    "rcParams.update({'xtick.minor.pad': '7.0'})\n",
    "rcParams.update({'xtick.minor.size': '3.5'})\n",
    "rcParams.update({'xtick.minor.width': '1.0'})\n",
    "rcParams.update({'ytick.major.pad': '7.0'})\n",
    "rcParams.update({'ytick.major.size': '7.5'})\n",
    "rcParams.update({'ytick.major.width': '1.5'})\n",
    "rcParams.update({'ytick.minor.pad': '7.0'})\n",
    "rcParams.update({'ytick.minor.size': '3.5'})\n",
    "rcParams.update({'ytick.minor.width': '1.0'})\n",
    "rcParams.update({'font.size': 30})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import dynesty"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the key assumptions of (Static) Nested Sampling is that we \"shrink\" according to\n",
    "\n",
    "$$ X_{i} = t_i X_{i-1} ~ , \\quad t_i \\sim \\textrm{Beta}(K, 1) $$\n",
    "\n",
    "at each iteration. We can empirically test this by using functions whose volumes can be analytically computed directly from the position of a sample. One example of this is the \"hyper-pyramid\" function whose log-likelihood is\n",
    "\n",
    "$$ \\ln \\mathcal{L} = - \\left( \\sup_i \\left| \\frac{x_i - \\frac{1}{2}}{\\sigma_i} \\right| \\right)^{1/s} $$\n",
    "\n",
    "where $s$ controls the \"slope\" and $\\sigma_i$ controls the \"scale\" in each dimension. Here we'll take $s=100$ and $\\sigma_i = \\sigma = 1$ following [Buchner (2014)](https://arxiv.org/abs/1407.5459)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define the eggbox log-likelihood\n",
    "s, sigma = 100., 1.\n",
    "def loglike(x):\n",
    "    return -max(abs((x - 0.5) / sigma))**(1. / s)\n",
    "\n",
    "# define the prior transform\n",
    "def prior_transform(x):\n",
    "    return x\n",
    "\n",
    "# plot the log-likelihood surface\n",
    "plt.figure(figsize=(10., 10.))\n",
    "axes = plt.axes(aspect=1)\n",
    "xx, yy = np.meshgrid(np.linspace(0., 1., 200),\n",
    "                     np.linspace(0., 1., 200))\n",
    "L = np.array([loglike(np.array([x, y]))\n",
    "              for x, y in zip(xx.flatten(), yy.flatten())])\n",
    "L = L.reshape(xx.shape)\n",
    "axes.contourf(xx, yy, L, 200, cmap=plt.cm.Purples_r)\n",
    "plt.title('Log-Likelihood Surface', y=1.01)\n",
    "plt.xlabel(r'$x$')\n",
    "plt.ylabel(r'$y$')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will now sample from this distribution using `'multi'`. We will change the defaults so that our bounding updates begin immediately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iter: 1501 | bound: 5 | nc: 1 | ncall: 3643 | eff(%): 41.202 | loglstar:   -inf < -0.979 <    inf | logz: -1.041 +/-  0.010 | dlogz:  0.054 >  0.010                                                  "
     ]
    }
   ],
   "source": [
    "ndim = 2\n",
    "nlive = 500\n",
    "sampler = dynesty.NestedSampler(loglike, prior_transform, ndim=ndim, bootstrap=50,\n",
    "                                first_update={'min_ncall': 0, 'min_eff': 100.},\n",
    "                                bound='multi', sample='unif', nlive=nlive)\n",
    "sampler.run_nested(dlogz=0.01, maxiter=1500, add_live=False)\n",
    "res = sampler.results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now compare the set of samples with the expected theoretical shrinkage. The contours for the bounding volume\n",
    "are given directly $\\mathcal{L}$ since $x_i = [r_0 − 1/2, r_0 + 1/2]$, where \n",
    "\n",
    "$$ r_0 = (- \\ln \\mathcal{L})^s = \\sup_i \\left| \\frac{x_i - \\frac{1}{2}}{\\sigma_i} \\right| $$\n",
    "\n",
    "The corresponding volume is a hyper-rectangle (N-cube) with\n",
    "\n",
    "$$ V = (2 \\cdot r_0)^d \\times \\prod_i \\sigma_i = (2 \\cdot r_0)^d \\quad .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The PDF of the shrinkage $t$ is\n",
    "\n",
    "$$ P(t \\,|\\, K) = (1-t)^{K-1} $$\n",
    "\n",
    "which has a CDF of \n",
    "\n",
    "$$ P(t < T \\,|\\, K) = t^K \\quad . $$\n",
    "\n",
    "Following Buchner (2014), we can define the quantity\n",
    "\n",
    "$$ s = 1 - t^{1/d} $$\n",
    "\n",
    "that represents the side being \"sliced\" away. This now has a cumulative distribution of\n",
    "\n",
    "$$ P(s < S) = 1 - (1 - S)^{dN} $$\n",
    "\n",
    "which is a bit easier to visualize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import kstest\n",
    "\n",
    "vol = (2 * (-res['logl'])**s)**ndim  # real volumes\n",
    "t = vol[1:] / vol[:-1]  # shrinkage\n",
    "S = 1 - t**(1. / ndim)  # slice\n",
    "\n",
    "# define our PDF/CDF\n",
    "def pdf(s):\n",
    "    return ndim * nlive * (1. - s)**(ndim * nlive - 1.)\n",
    "def cdf(s):\n",
    "    return 1. - (1. - s)**(ndim * nlive)\n",
    "\n",
    "# check whether the two distributions are consistent\n",
    "k_dist, k_pval = kstest(S, cdf)\n",
    "\n",
    "# plot results\n",
    "xgrid = np.linspace(0., 0.1, 10000)\n",
    "\n",
    "# PDF\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 6))\n",
    "ax = axes[0]\n",
    "pdfgrid = pdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step', \n",
    "                  color='navy', density=True, lw=4, label='Samples')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 5])\n",
    "ax.set_ylabel('PDF')\n",
    "ax.legend()\n",
    "\n",
    "# CDF\n",
    "ax = axes[1]\n",
    "cdfgrid = cdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step',\n",
    "                  cumulative=True, color='navy', \n",
    "                  density=True, lw=4, label='Theory')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, cumulative=True,\n",
    "        histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 5])\n",
    "ax.set_ylabel('CDF')\n",
    "ax.text(0.95, 0.2, 'dist: {:6.3}'.format(k_dist), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "ax.text(0.95, 0.1, 'p-value: {:6.3}'.format(k_pval), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's turn bootstrapping off."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iter: 1501 | bound: 5 | nc: 4 | ncall: 3981 | eff(%): 37.704 | loglstar:   -inf < -0.978 <    inf | logz: -1.041 +/-  0.010 | dlogz:  0.053 >  0.010                                                  "
     ]
    }
   ],
   "source": [
    "ndim = 2\n",
    "sampler = dynesty.NestedSampler(loglike, prior_transform, ndim=ndim,\n",
    "                                bound='multi', sample='unif', nlive=nlive,\n",
    "                                first_update={'min_ncall': 0, 'min_eff': 100.})\n",
    "sampler.run_nested(dlogz=0.01, maxiter=1500, add_live=False)\n",
    "res = sampler.results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vol = (2 * (-res['logl'])**s)**ndim  # real volumes\n",
    "t = vol[1:] / vol[:-1]  # shrinkage\n",
    "S = 1 - t**(1. / ndim)  # slice\n",
    "\n",
    "# check whether the two distributions are consistent\n",
    "k_dist, k_pval = kstest(S, cdf)\n",
    "\n",
    "# PDF\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 6))\n",
    "ax = axes[0]\n",
    "pdfgrid = pdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step', \n",
    "                  color='dodgerblue', density=True, lw=4, label='Samples')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 5])\n",
    "ax.set_ylabel('PDF')\n",
    "ax.legend()\n",
    "\n",
    "# CDF\n",
    "ax = axes[1]\n",
    "cdfgrid = cdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step',\n",
    "                  cumulative=True, color='dodgerblue', \n",
    "                  density=True, lw=4, label='Theory')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, cumulative=True,\n",
    "        histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 5])\n",
    "ax.set_ylabel('CDF')\n",
    "ax.text(0.95, 0.2, 'dist: {:6.3}'.format(k_dist), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "ax.text(0.95, 0.1, 'p-value: {:6.3}'.format(k_pval), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that without incorporating the bootstrap expansion factors the ellipsoids have a tendency to over-constrain the remaining prior volume and shrink too quickly. What happens if we increase the number of dimensions?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iter: 1501 | bound: 13 | nc: 5 | ncall: 9700 | eff(%): 15.474 | loglstar:   -inf < -0.989 <    inf | logz: -1.044 +/-  0.010 | dlogz:  0.052 >  0.010                                                 "
     ]
    }
   ],
   "source": [
    "ndim = 7\n",
    "sampler = dynesty.NestedSampler(loglike, prior_transform, ndim=ndim, bootstrap=50,\n",
    "                                bound='multi', sample='unif', nlive=nlive, \n",
    "                                first_update={'min_ncall': 0, 'min_eff': 100.})\n",
    "sampler.run_nested(dlogz=0.01, maxiter=1500, add_live=False)\n",
    "res = sampler.results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vol = (2 * (-res['logl'])**s)**ndim  # real volumes\n",
    "t = vol[1:] / vol[:-1]  # shrinkage\n",
    "S = 1 - t**(1. / ndim)  # slice\n",
    "\n",
    "# check whether the two distributions are consistent\n",
    "k_dist, k_pval = kstest(S, cdf)\n",
    "\n",
    "# PDF\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 6))\n",
    "ax = axes[0]\n",
    "pdfgrid = pdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step', \n",
    "                  color='navy', density=True, lw=4, label='Samples')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('PDF')\n",
    "ax.legend()\n",
    "\n",
    "# CDF\n",
    "ax = axes[1]\n",
    "cdfgrid = cdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step',\n",
    "                  cumulative=True, color='navy', \n",
    "                  density=True, lw=4, label='Theory')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, cumulative=True,\n",
    "        histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('CDF')\n",
    "ax.text(0.95, 0.2, 'dist: {:6.3}'.format(k_dist), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "ax.text(0.95, 0.1, 'p-value: {:6.3}'.format(k_pval), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iter: 1501 | bound: 5 | nc: 1 | ncall: 4087 | eff(%): 36.726 | loglstar:   -inf < -0.988 <    inf | logz: -1.044 +/-  0.010 | dlogz:  0.052 >  0.010                                                  "
     ]
    }
   ],
   "source": [
    "ndim = 7\n",
    "sampler = dynesty.NestedSampler(loglike, prior_transform, ndim=ndim,\n",
    "                                bound='multi', sample='unif', nlive=nlive, \n",
    "                                first_update={'min_ncall': 0, 'min_eff': 100.})\n",
    "sampler.run_nested(dlogz=0.01, maxiter=1500, add_live=False)\n",
    "res = sampler.results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vol = (2 * (-res['logl'])**s)**ndim  # real volumes\n",
    "t = vol[1:] / vol[:-1]  # shrinkage\n",
    "S = 1 - t**(1. / ndim)  # slice\n",
    "\n",
    "# check whether the two distributions are consistent\n",
    "k_dist, k_pval = kstest(S, cdf)\n",
    "\n",
    "# PDF\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 6))\n",
    "ax = axes[0]\n",
    "pdfgrid = pdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step', \n",
    "                  color='dodgerblue', density=True, lw=4, label='Samples')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('PDF')\n",
    "ax.legend()\n",
    "\n",
    "# CDF\n",
    "ax = axes[1]\n",
    "cdfgrid = cdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step',\n",
    "                  cumulative=True, color='dodgerblue', \n",
    "                  density=True, lw=4, label='Theory')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, cumulative=True,\n",
    "        histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('CDF')\n",
    "ax.text(0.95, 0.2, 'dist: {:6.3}'.format(k_dist), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "ax.text(0.95, 0.1, 'p-value: {:6.3}'.format(k_pval), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, these trends get substantially worse as we move to higher dimensions. To mitigate this trend, in addition to bootstrapping ``dynesty`` also incorporates a built-in enlargement factor to increase the size of the bounding ellipsoids, as well as a more conservative decomposition algorithm. Ultimately, however, the better approach is to use a sampling method that is less sensitive to the bounding distributions, as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "iter: 1501 | bound: 12 | nc: 20 | ncall: 40607 | eff(%):  3.696 | loglstar:   -inf < -0.989 <    inf | logz: -1.044 +/-  0.010 | dlogz:  0.052 >  0.010                                               "
     ]
    }
   ],
   "source": [
    "ndim = 7\n",
    "sampler = dynesty.NestedSampler(loglike, prior_transform, ndim=ndim,\n",
    "                                bound='multi', sample='rslice', nlive=nlive, \n",
    "                                first_update={'min_ncall': 0, 'min_eff': 100.})\n",
    "sampler.run_nested(dlogz=0.01, maxiter=1500, add_live=False)\n",
    "res = sampler.results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "vol = (2 * (-res['logl'])**s)**ndim  # real volumes\n",
    "t = vol[1:] / vol[:-1]  # shrinkage\n",
    "S = 1 - t**(1. / ndim)  # slice\n",
    "\n",
    "# check whether the two distributions are consistent\n",
    "k_dist, k_pval = kstest(S, cdf)\n",
    "\n",
    "# PDF\n",
    "fig, axes = plt.subplots(1, 2, figsize=(20, 6))\n",
    "ax = axes[0]\n",
    "pdfgrid = pdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step', \n",
    "                  color='gray', density=True, lw=4, label='Samples')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('PDF')\n",
    "ax.legend()\n",
    "\n",
    "# CDF\n",
    "ax = axes[1]\n",
    "cdfgrid = cdf(xgrid)\n",
    "n, b, p = ax.hist(S * 1e3, bins=50, histtype='step',\n",
    "                  cumulative=True, color='gray', \n",
    "                  density=True, lw=4, label='Theory')\n",
    "ax.hist(xgrid * 1e3, bins=b, color='red', density=True,\n",
    "        weights=pdfgrid, lw=4, cumulative=True,\n",
    "        histtype='step', label='Theory')\n",
    "ax.set_xlabel('Shrinkage [1e-3]')\n",
    "ax.set_xlim([0., 1.5])\n",
    "ax.set_ylabel('CDF')\n",
    "ax.text(0.95, 0.2, 'dist: {:6.3}'.format(k_dist), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "ax.text(0.95, 0.1, 'p-value: {:6.3}'.format(k_pval), \n",
    "        horizontalalignment='right', verticalalignment='center',\n",
    "        transform=ax.transAxes)\n",
    "\n",
    "plt.tight_layout()"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
